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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 595360, 12 pages
http://dx.doi.org/10.1155/2012/595360
Research Article

Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators

1College of Science, Guilin University of Technology, Guilin 541004, China
2Guangxi Key Laboratory of Spatial Information and Geomatics, Guilin 541004, China

Received 14 March 2012; Accepted 15 June 2012

Academic Editor: Jitao Sun

Copyright © 2012 Zhen Jia and Guangming Deng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a mathematical model of a complex dynamical network consisting of two types of chaotic oscillators and investigate the schemes and corresponding criteria for cluster synchronization. The global asymptotically stable criteria for the linearly or adaptively coupled network are derived to ensure that each group of oscillators is synchronized to the same behavior. The cluster synchronization can be guaranteed by increasing the inner coupling strength in each cluster or enhancing the external excitation. Theoretical analysis and numerical simulation results show that the external excitation is more conducive to the cluster synchronization. All of the results are proved rigorously. Finally, a network with a scale-free subnetwork and a small-world subnetwork is illustrated, and the corresponding numerical simulations verify the theoretical analysis.